# Faces Vertices Worksheet - Excel by wwm18296

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```									GEOMETRY                    PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                  2010 - 2011
Module 1       Start: 8/19/2010 Teaching Days: 27               Test: 9/27/2010        Remediation Days: 1 End: 9/24/2010
Student Learning Expectation                                                       Task Analysis                                                 Vocabulary
1. Enduring Understanding - Points, lines, and planes are the foundations of geometry.
1a. Essential Question - Why are the following considered to be undefined terms in geometry: point, line, and plane?
LG.1.G.2                  Represent points, lines, and planes pictorally *identify points, lines, segments, rays, angles, and planes using models         point
with proper identification, as well as basic   *draw, label, and use proper symbol notation to represent the undefined          line
concepts derived from these undefined terms, terms points, lines, and planes in addition to rays, segments, and angles          plane
such as segments, rays, and angles                                                                                              segment
ray
angle
conjecture
colinear points
coplanar points
National Core:            G.CO.1                                           Know precise definitions of angle, circle, perpendicular line, parallel
line, and line segment, based on the undefined notions of point, line,
distance along a line, and distance around a circular arc.

Resources:                G. 1-1 pg.6; 1-4 pg.29; supplemental-origami box; wkst Drawing Intersections;          MCO---Students will give examples of points, lines, and planes and
relationships ofgeometric figures (parallel, perpendicular, angle relationships, etc) from objects found in nature. Students will bring items to class and have
classmates identify the term being modeled.

Assessments:
LG.1.G.4                  Apply, with and without appropriate              *define and identify complementary angles, supplementary angles,               theorem
technology, definitions, theorems, properties,   vertical angles, linear pair of angles, and right angles                       postulate
and postulates related to such topics as         *determine relationships between angles formed by intersecting lines           corollary
complementary, supplementary, vertical           *find measures of angles using relationships                                   complementary angles
angles, linear pairs, and angles formed by       *use technology (scientific calculator, graphing calculator, Geogebra, etc.)   supplementary angles
perpendicular lines                              to reinforce concepts                                                          vertical angles
consecutive angles
linear pair of angles
perpendicular lines
right angles

Resources:                G. 1-5 pg.37; MCO---Use ceiling tiles numbered and lettered for each type angle, later to be used for transversals; wkst. Angles and the Hands of Time;
Finding Missing Angles; Measuring Angles with a Protractor; later with chapter 4

Assessments:
Page 1 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
2. Enduring Understanding - Geometric figures can be represented in the coordinate plane.
2a. Essential Question - How can the relationships of lines be verified using the coordinate plane?
CGT.5.G.1a             Use coordinate geometry to find the distance   *calculate the midpoint and distance on the number line and between two      coordinate geometry
between two points and the midpoint of a       points                                                                       coordinate plane
segment                                        *calculate the midpoint and distance between two points on the               midpoint of a segment
coordinate plane                                                             distance formula
midpoint formula

National Core:         G.PE.4                                         Use coordinates to prove simple geometric theorems algebraically. For
example, prove or disprove that a figure defined by four given points in
the coordinate plane is a rectangle; prove or disprove that the point (1,
√3) lies on the circle centered at the origin and containing the point (0,
2).

G.PE.5                                         Prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems (e.g., find the equation of a line
parallel or perpendicular to a given line that passes through a given
point).

Resources:             G. 1-3 pg.21; wkst Positioning Streets on a Map

Assessments:
3. Enduring Understanding - Valid inductive and deductive reasoning are used to develop and prove conjectures.

3a. Essential Question - How does the application of logical reasoning facilitate understanding real-world situations?
LG.1.G.1a              Define inductive and deductive reasoning       *define inductive and deductive reasoning                                    inductive reasoning
deductive reasoning

Resources:             G. 2-1 pg.62 2-4 pg.82 deductive reasoning (omit laws of detachment, syllogism, and truth tables); wkst. Calculator Digits-Perpendicular and Parallel
Segments; NUMBER PATTERNS;

Assessments:

Page 2 of 40                                                              Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
LG.1.G.1b                 Make predictions or conjectures based on real     *extend patterns by various strategies                                   inductive reasoning
world situations using inductive reasoning        *make conclusions based on real world situations                         pattern
such as but not limited to:                       *make conjetures by various strategies including figural and numerical
* Using figural and numerical patterns            patterns
* Using observations
* Identifying counterexamples

Resources:                G. 2-1 pg.63 problems pg.64 Ch.2 Resource Enrichment pg.62

Assessments:
LG.1.G.1c                 Make predictions or conjectures based on real     *read Venn diagrams                                                      inductive reasoning
world situations using deductive reasoning        *read a logic matrix                                                     deductive reasoning
and appropriate strategies such as but not        *draw and interpret Venn diagrams                                        Venn diagram
limited to: • Venn diagrams • Matrix logic        *draw and use logic matrix to state conclusions                          matrix logic
*make conclusions based on real world situations                         conjecture

Resources:                G. pg.88 pg.69-70 problem pg.73 #41-44,Manipulatlives pg.46 Ch.2 Resource Enrichment pg.80; wkst. supplements;VENN FAMILY;             MCO----Students will
work in pairs to solve matrix logic puzzles and draw Venn diagrams.

Assessments:
LG.1.G.1d                 Make predictions or conjectures based on real     *identify examples of Laws of Syllogism and Laws of Detachment           inductive reasoning
world situations using inductive and/or           *extend patterns by various strategies                                   deductive reasoning
deductive reasoning strategies such as but not    *write inverse, converse, and contrapositive when given a statement      conditional statement
limited to:                                       *determine equivalence of statement & contrapositive and of converse &   inverse
* Conditional statements (statement,              inverse                                                                  converse
converse, inverse, contrapositive)                *make conclusions based on real world situations                         contrapositive
* Laws of Syllogism and Laws of Detachment                                                                                 counterexample
* Identifying valid and invalid conclusions and                                                                            biconditional statement
arguments                                                                                                                  negation

Resources:                G. 2-3 pg.75 Manipulatives pg.41 Ch.2 Resource Enrichment pg.74; MCO---Student will work in groups to practice conditional statements. Students will
take turns writing a statement and the other members of the group will write the converse, inverse, and contrapositive.

Assessments:
LG.1.G.3                  Describe relationships derived from geometric *identify figural patterns                                                   figural pattern
figures or figural patterns                   *extend patterns using various strategies                                    sequences
*describe pattern relationships with symbols, words, and pictures

Page 3 of 40                                                                Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
Resources:                vocabulary review Ch.1 Resource pg.50; example problems Ch.1 Angle Relationships pg.26; wkst. Figurate Numbers; wkst. Pascal's Triangle

Assessments:
LG.1.G.6                  Give justification for conclusions reached by   *state basic theorems                                                       two-column proof
deductive reasoning; State and prove key        *justify or construct a basic proof, whether two-column, paragraph, or      paragraph proof
basic theorems in geometry (i.e., the           flow                                                                        flow proof
Pythagorean Theorem, the sum of the                                                                                         justify
measures of the angles of a triangle is 180°,
and the line joining the midpoints of two sides
of a triangle is parallel to the third side and
half its length)

National Core:            G.CO.9                                         Prove theorems about lines and angles. Theorems include: vertical
angles are congruent; when a transversal crosses parallel lines, alternate
interior angles are congruent and corresponding angles are congruent;
points on a perpendicular bisector of a line segment are exactly those
equidistant from the segment’s endpoints.

G.CO.10                                        Prove theorems about triangles. Theorems include: measures of interior
angles of a triangle sum to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides of a triangle is
parallel to the third side and half the length; the medians of a triangle
meet at a point.

Resources:                G. 2-5 pg.89; 2-6 pg.94; 2-7 pg.101; 2-8 pg.107; SCHOOL MATH; LINEUP LOGIC; MYSTERIES;            MCO----Students will be given an algebraic proof with
the statements and reason cut apart. Students will then reconstruct the proof by matching the statement with the correct property of equality and put
them in order.

Assessments:
9 SLEs                                                                                                                                                                   End of Module 1

ALIGNMENT NOTES
Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together

Page 4 of 40                                                              Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
Project for Quarter 1

The Angle Book Project
1. Make a foldable book following directions given.
2. Use example book as guide for students.
3. Use two days of classtime, due at latter part of 1st qtr.

Page 5 of 40                                              Glencoe Geometry: 2005   127rgeorge@pcssdmail.org
GEOMETRY                 PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                    2010 - 2011
Module 2     Start: 9/27/2010 Teaching Days: 22                Test: 11/1/2010          Remediation Days: 1 End: 10/20/2010
Student Learning Expectation                                                          Task Analysis                                                 Vocabulary
1. Enduring Understanding - Points, lines, and planes are the foundations of geometry.
1b. Essential Question - How can angle relationships be used to prove that two lines cut by a transversal are parallel?
LG.1.G.5a              Solve problems involving the parallel                *identify angle pairs created by parallel lines cut by a transversal          parallel lines
relationship of two lines in a plane that are cut    *deduce that vertical angles, corresponding angles, alternate interior        transversal
by a transversal                                     angles, and alternate exterior angles are congruent, and that same side       corresponding angles
•a pair of alternate interior, alternate exterior,   interior/exterior angles are supplementary                                    alternate interior/exterior angles
or corresponding angles are congruent                *use angle relationships to find missing angle measures                       same-side interior (consecutive
•consecutive (same-side) interior angles are         *use angle relationships to prove two lines cut by a transversal are          interior)
supplementary                                        parallel                                                                      same-side exterior (consecutive
•consecutive (same-side) exterior angles are         *use technology (scientific/graphing calculator, geogebra, etc) to teach or   exterior)
supplementary                                        reinforce concepts                                                            supplementary angles
congruent
skew lines

Resources:             G. 3-1 pg.126; use ceiling tiles with colored painters tape

Assessments:
LG.1.G.5b              Solve problems involving the parallel            *identify angle pairs created by parallel lines cut by a transversal              parallel lines
relationship of two lines that are perpendicular *determine that vertical angles, corresponding angles, alternate interior         perpendicular lines
to the same line                                 angles, and alternate exterior angles are congruent, and that same side           transversal
interior/exterior angles are supplementary                                        corresponding angles
*use angle relationships to find missing angle measures                           alternate interior/exterior angles
*use angle relationships to prove two lines cut by a transversal are              same-side interior (consecutive
parallel                                                                          interior)
*determine that two lines perpendicular to the same line are parallel             same-side exterior
*solve problems with two lines perpendicular to the same lines being              supplementary angles
parallel                                                                          congruent
*use technology to reinforce concepts                                             skew lines

Resources:             G. 3-4 pg.134; Monopoly and Perpendicular and Parallel Lines; BUILD IT

Assessments:
2. Enduring Understanding - Geometric figures can be represented in the coordinate plane.
2b. Essential Question - How can the relationships of lines be verified using the coordinate plane?

Page 6 of 40                                                                    Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
CGT.5.G.1b             Use coordinate geometry to find the slopes of *determine the slope of a line using two points                                    coordinate geometry
parallel, perpendicular, horizontal, and vertical *determine the relationships of slopes of parallel and perpendicular lines,    coordinate plane
lines                                             and determine if lines are parallel, perpendicular, or intersecting            slope
*distinguish when the graph of a line is vertical or horizontal based on       slope of parallel lines
slope                                                                          slope of perpendicular lines
slope of horizontal lines
slope of vertical lines
slope formula
negative reciprocal

National Core:         G.PE.4                                            Use coordinates to prove simple geometric theorems algebraically. For
example, prove or disprove that a figure defined by four given points in
the coordinate plane is a rectangle; prove or disprove that the point (1,
√3) lies on the circle centered at the origin and containing the point (0,
2).

G.PE.5                                            Prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems (e.g., find the equation of a line
parallel or perpendicular to a given line that passes through a given
point).

Resources:             G. 3-3 pg.139; 3-4 pg.145

Assessments:
CGT.5.G.2              Write the equation of a line parallel to a line   *determine the slope of the line parallel to a given line                      slope of parallel lines
through a given point not on the line             *use slope-intercept form or point-slope form to determine the y-intercept     slope-intercept form of a linear
(b)                                                                            equation
*write the equation of the line parallel to the given line through the given   standard form of a linear
point in all possible forms                                                    equation
point-slope form of a linear
equation
Resources:             G. 3-3 pg.139; 3-4 pg.145

Assessments:
CGT.5.G.3              Write the equation of a line perpendicular to a *determine the slope of the line perpendicular to a given line                   slope of perpendicular lines
line through a given point                      *use slope-intercept form or point-slope form to determine the y-intercept       slope-intercept form of a linear
(b)                                                                              equation.
*write the equation of the line perpendicular to the given line through the      standard form of a linear
given point in all possible forms                                                equation
point-slope form of a linear
equation

Page 7 of 40                                                                 Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
Resources:                G. 3-3 pg.139; 3-4 pg.145

Assessments:
4. Enduring Understanding - Similar geometric figures have proportional attributes
4a. Essential Question - How are relationships between congruent figures used to solve problems?
T.2.G.1a                  Apply SSS, SAS, ASA, AAS congruence           *identify properties of congruent figures                                  congruent polygons
correspondence to find missing parts of       *identify corresponding parts of triangles                                 corresponding parts
geometric figures and provide logical         *use theorems to prove triangles congruent                                 side angle side congruence
justification                                 *use proportions to find missing sides of figures                          angle side angle congruence
*use properties to find missing angles                                     side side side congruence
angle angle side congruence

National Core:            G.CO.7                                        Explain and use the relationship between the sine and cosine of
complementary angles.

Resources:                G. 4-4 pg.200; 4-5 pg.207; wkst. The Big Triangle Problem; wkst Angles of Triangles; wkst. Identifying what is needed to prove triangles are congruent;
patty paper wkst 126-139, 168,199

Assessments:
5 SLEs                                                                                                                                                                End of Module 1

ALIGNMENT NOTES
Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together

Project for Module 2

Page 8 of 40                                                             Glencoe Geometry: 2005                                                127rgeorge@pcssdmail.org
GEOMETRY                    PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                 2010 - 2011
Module 3           Teaching Days: 25 Test: 12/16/2010                Remediation Days: 1       End: 12/10/2010
Student Learning Expectation                                                       Task Analysis                                                Vocabulary
5. Enduring Understanding - Relationships that exist between the angles and sides of geometric figures can be
proven.
5a. Essential Question - How are properties of geometric figures related to their measurable attributes?
T.2.G.3a                  Identify and use the altitudes of triangles to   *identify altitude                                                             altitude of a triangle
solve problems                                   *state conclusions about angle measures and segment lengths when               orthocenter
drawing altitudes                                                              perpendicular
*apply concepts to basic proofs                                                geometric mean
*examine orthocenters of various types of triangles
*solve problems using properties of altitudes

National Core:            G.CO.12                                          Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the
line.

Resources:                G. 5-1 pg.238; patty paper wkst 37and 47

Assessments:
T.2.G.3b                  Identify and use the medians of triangles to     *identify median                                                               median of a triangle
solve problems                                   *state conclusions about angle measures and segment lengths when               centroid
drawing medians
*solve problems using properties of medians
*examine centroids of various types of triangles
*apply concepts to basic proofs

National Core:            G.CO.12                                          Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the
line.

Page 9 of 40                                                                Glencoe Geometry: 2005                                                    127rgeorge@pcssdmail.org
Resources:                 G. 5-1 pg.238; wkst. Medians of Triangles; patty paper wkst 36

Assessments:
T.2.G.3c                   Identify and use the angle bisectors of        *identify angle bisector                                                       angle bisector
triangles to solve problems                    *state conclusions about angle measures and segment lengths when               incenter
drawing angle bisectors
*solve problems using properties of angle bisectors
*examine incenters of various types of triangles
*apply concepts to basic proofs

National Core:             G.CO.12                                        Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the
line.

Resources:                 G. 5-1 pg.238; patty paper wkst 34 and 45; MCO----Students will use quilt patterns, mosaics, or other artwork from various cultures to identify triangles
and the special segments of the triangles. Students my choose to create their own artwork using triangles and their segments.

Assessments:
T.2.G.3d                   Identify and use the perpendicular bisectors of *identify perpendicular bisector                                              perpendicular bisector
triangles to solve problems                     *state conclusions about angle measures and segment lengths when              circumcenter
drawing perpendicular bisectors
*solve problems using properties of perpendicular bisectors
*examine circumcenters of various types of triangles
*apply concepts to basic proofs

National Core:             G.CO.12                                        Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the
line.

Resources:                 G. 5-1 pg.238; wkst. Triangles: The Points, Segments, and Angles; patty paper wkst 32 and wkst 43;       MCO---- Students will work with a partner and use
straws to build trianagles with special segments.

Page 10 of 40                                                              Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
Assessments:
T.2.G.3e                   Identify and use the midsegments of triangles *identify midsegment                                                              midsegment
to solve problems                             *state conclusions about angle measures and segment lengths when
drawing midsegments
*solve problems using properties of midsegments
*apply concepts to basic proofs

National Core:             G.CO.12                                          Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the
line.

Resources:                 G. pg.308; wksht Triangles: the points, segments, and angles; patty paper wkst 74

Assessments:
5b. Essential Question - How can it be determined if three given segment measures will form a triangle?
T.2.G.2                    Investigate the measures of segments to          *create triangles using lengths of line segments                               Triangle Inequality Theorem
determine the existence of triangles (triangle   *investigate the measures of segments to determine the existence of
inequality theorem)                              triangles
*state conclusions when applying the Triangle Inequality Theorem

Resources:                 G. 5-2 pg.247; 5-4 pg.261; spaghetti and paper

Assessments:
4. Enduring Understanding - Indirect measurement is based on the properties of geometric figures.
4b. Essential Question - How are the relationships between similar figures used to solve problems?
M.3.G.4                    Given similar geometric objects, use             *identify properties of similar figures                                        similar figures/polygons
proportional reasoning to solve practical        *determine if figures are similar by setting up and solving proportions        scale drawing
problems (including scale drawings)              *use scale drawings and other information to solve real-world problems         geometric mean
through proportional reasoning

Page 11 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
National Core:           G.SRT.4                                         Prove theorems about triangles. Theorems include: a line parallel to one
side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.

G.SRT.5                                         Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
G.GPE.6                                         Find the point on a directed line segment between two given points
that partitions the segment in a given ratio.

G.MG.3                                          Apply geometric methods to solve design problems (e.g., designing
an object or structure to satisfy physical constraints or minimize cost;
working with typographic grid systems based on ratios).

Resources:               G. 6-2 pg.289; 6-3 pg.298; teacher to teacher pg.291; STICK FIGURES

Assessments:
M.3.G.5a                 Identify and apply properties of and theorems *apply angle relationships of parallel lines cut by a transversal                parallel lines
about parallel and perpendicular lines to prove *apply angle relationships of perpendicular lines                              perpendicular lines
other theorems                                  *identify properties and theorems of parallel and perpendicular lines          theorems
*prove theorems related to parallel and perpendicular lines

National Core:           G.SRT.4                                         Prove theorems about triangles. Theorems include: a line parallel to one
side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.

Resources:               G. 6-4 pg. 307: PATTERN BLOCKS

Assessments:
8 SLEs                                                                                                                                                                    End of Module 1

ALIGNMENT NOTES
Notation
G.- Glencoe Textbook;
Project for Module 3

Page 12 of 40                                                               Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
GEOMETRY                     PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                2010 - 2011
Module 4       Start: 1/3/2011 Teaching Days: 25                Test: 2/10/2011       Remediation Days: 1 End: 2/4/2011
Student Learning Expectation                                                       Task Analysis                                                  Vocabulary
4. Enduring Understanding - Indirect measurement is based on the properties of geometric figures.
4c. Essential Question - How are properties of right triangles used to find angle and side measurements?
T.2.G.4                    Apply the Pythagorean Theorem and its           *identify legs and hypotenuse of a right triangle                             Pythagorean Theorem
converse in solving practical problems          *solve equations using Pythagorean Theorem                                    hypotenuse
*use Pythagorean Theorem to solve practical problems and express in           leg
*given a, b and c, determine if a triangle is a right triangle given the
lengths of the sides

National Core:             G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.

Resources:                 G. 7-2 pg.350; geoboard; wkst. The Pythagorean Theorem; wkst. What Type of Triangle?; MCO----Students will work in groups to draw right triangles to
solve real world problems that they have created. After the students in the group agree on the way to set up the problem each student will then apply the
Pythagorean Theorem or trignometic ratio to solve.

Assessments:
T.2.G.5a                   Use the special right triangle relationship 30°- *describe the relationships between the length of sides of 30°-60°-90°       special right triangle
60°-90° to solve problems                        triangles
*find the length of two sides of a 30°-60°-90° triangle when one side is
given
*apply the relationships of a 30°-60°-90° triangle to find missing side(s)
and angle(s) in diagrams and word problems

Resources:                 G. 7-3 pg.357

Assessments:
T.2.G.5b                   Use the special right triangle relationship 45°- *describe the relationships between the length of sides of 45°-45°-90°       special right triangle
45°-90° to solve problems                        triangles
*find the length of two sides of a 45°-45°-90° triangle when one side is
given
*apply the relationships of a 45°-45°-90° triangle to find missing side(s)
and angle(s) in diagrams and word problems
*use the Isosceles Triangle Theorem and the Pythagorean Theorem to
determine the lengths of sides of special right triangles

Page 13 of 40                                                               Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
Resources:                 G. 7-3 pg.357 daily intervention differentiated instruction pg.358; wkst Right Triangles and Special Right Triangles

Assessments:
T.2.G.6a                   Use trigonometric ratios (sine, cosine,         *apply trigonometric ratios of a right triangle given the length of one side trigonometric ratios
tangent) to determine lengths of sides in right and the measures of one acute angle to find the lengths of sides in right sine
triangles                                       triangles in giagrams and real-world problems                                cosine
tangent
hypotenuse
leg of a right triangle
opposite side

National Core:             G.SRT.7                                         Explain and use the relationship between the sine and cosine of
complementary angles.

G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.

Resources:                 G. 7-4 pg.364 Manipulatives pg.117-120

Assessments:
T.2.G.6b                   Use trigonometric ratios (sine, cosine,         *apply trigonometric ratios given two sides and an angle measure in           trigonometric ratios
tangent) to determine measures of angles in     diagrams and real-world problems                                              sine
right triangles                                                                                                               cosine
tangent
hypotenuse
leg of a right triangle
opposite side

National Core:             G.SRT.7                                         Explain and use the relationship between the sine and cosine of
complementary angles.

G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Resources:                 G. 7-4 pg.364 Manipulatives pg.117-120

Assessments:

Page 14 of 40                                                                Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
T.2.G.6c                   Use trigonometric ratios (sine, cosine,         *identify angles of elevation and angles of depression                     trigonometric ratios
tangent) in right triangle problems involving   *use trig ratios to find side lengths and or angles of elevation or        sine
angles of elevation and depression              depression in diagrams and real-world problems                             cosine
tangent
angle of elevation
angle of depression
hypotenuse
leg of a right triangle
opposite side

National Core:             G.SRT.7                                         Explain and use the relationship between the sine and cosine of
complementary angles.

G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.

Assessments:
T.2.G.7                    Use similarity of right triangles to express the *identify similar triangle characteristics                                similarity
sine, cosine, and tangent of an angle in a right *set up proportions from similar triangles to find missing side lengths   sine
triangle as a ratio of given side lengths        *write trig ratios of similar triangles                                   cosine
tangent
angle of elevation
angle of depression

National Core:             G.SRT.6                                         Understand that by similarity, side ratios in right triangles are
properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.

Resources:                 G. pg. 214-215

Assessments:
5. Enduring Understanding - Relationships exist between the angles and sides of geometric figures.
5a. Essential Question - How are angles, sides, and diagonals of quadrilaterals related and applied?

Page 15 of 40                                                                Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
R.4.G.1a                   Explore, verify and solve problems involving     *identify properties of quadrilaterals                                      quadrilaterals
the properties of quadrilaterals                 *determine properties of quadrilaterals with respect to parallel sides,     parallelograms
• Four sided polygon                             lengths of sides, diagonal measurements, and measurement of angles          rectangle
*explore quadrilaterals and their properties to verify the type of figure   rhombus
formed                                                                      square
*solve problems involving the properties of quadrilaterals                  trapezoid
kite
isosceles trapezoid
consecutive sides/angles
opposite sides/angles
midsegments

National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
sides are congruent, opposite angles are congruent, the diagonals
of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.

Assessments:
R.4.G.1b                   Explore, verify and solve problems involving     *identify properties of parallelograms                                      quadrilaterals
the properties of parallelograms                 *determine properties of parallelograms with respect to parallel sides,     diagonals
• Quadrilateral                                  length of sides, diagonal measurements, and measurement of angles           parallelograms
• Congruent opposite sides and opposite          *explore parallelograms and their properties to verify the type of figure   consecutive sides/angles
angles                                           formed                                                                      opposite sides/angles
• Consecutive angles are supplementary                                                                                       supplementary
• Diagonals bisect                                                                                                           bisect
• Two congruent triangles are formed by the
diagonals
• If there is one right angle, then all angles
are right angles.

National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
sides are congruent, opposite angles are congruent, the diagonals
of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.

Resources:                 G. 8-2 pg.411; Manipulatives pg.129;     MCO--- Students will investigate the clothing of various cultures looking for geometric designs that form different
polygons.

Page 16 of 40                                                                Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
Assessments:
R.4.G.1c                   Explore, verify and solve problems involving     *identify properties of parallelograms                                         quadrilaterals
the proof that a quadrilateral is a              *determine properties of parallelograms with respect to parallel sides,        parallelograms
parallelogram                                    length of sides, diagonal measurements, and measurement of angles              consecutive sides/angles
• Diagonals bisect each other                    *explore parallelograms and their properties to verify the type of figure      opposite sides/angles
• One pair of opposite sides is both congruent   formed                                                                         diagonals
and parallel                                                                                                                    bisect
• Both pairs of opposite sides are congruent
• Both pairs of opposide sides are parallel
• Both pairs of opposite angles are congruent

National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
sides are congruent, opposite angles are congruent, the diagonals
of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.

Resources:                 G. 8-3 pg.417; Manipulatives pg.132; Ch.2 Enrichment pg.434

Assessments:
R.4.G.1d                   Explore, verify and solve problems involving     *identify properties of rectangles                                             quadrilaterals
the properties of rectangles                     *determine properties of rectangles with respect to parallel sides, length     parallelograms
• Same properties as parallelograms              of sides, diagonal measurements, and measurement of angles                     rectangle
• Four right angles                              *explore rectangles and their properties to verify the type of figure formed   consecutive sides/angles
• Congruent diagonals                                                                                                           opposite sides/angles
diagonals

National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
sides are congruent, opposite angles are congruent, the diagonals
of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.
Assessments:
R.4.G.1e                   Explore, verify and solve problems involving     *identify properties of rhombi                                                 quadrilaterals
the properties of rhombi                         *determine properties of rhombi with respect to parallel sides, length of      parallelograms
• Same properties as parallelograms              sides, diagonal measurements, and measurement of angles                        rectangle
• All sides are congruent                        *explore rhombi and their properties to verify the type of figure formed       rhombus
• Diagonals are perpendicular                                                                                                   consecutive sides/angles
• Diagonlas bisect a pair of opposite angles                                                                                    opposite sides/angles
diagonal
perpendicular
bisect
Page 17 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
sides are congruent, opposite angles are congruent, the diagonals
of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.

Resources:                 G. 8-5 pg.431; Ch.8 Resources pg.445

Assessments:
R.4.G.1f                   Explore, verify and solve problems involving     *identify properties of squares                                                quadrilaterals
the properties of squares                        *determine properties of squares with respect to parallel sides, length of     parallelograms
• Same properties as parallelograms              sides, diagonal measurements, and measurement of angles                        rectangle
• Same properties as rectangles                  *explore squares and their properties to verify the type of figure formed      rhombus
• Same properties as rhombi                                                                                                     square
consecutive sides/angles
opposite sides/angles
diagonals
bisect
perpendicular

National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
sides are congruent, opposite angles are congruent, the diagonals
of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.

Resources:                 G. 8-5 pg.431; Manipulatives pg.135

Assessments:
R.4.G.1g                   Explore, verify and solve problems involving     *identify properties of trapezoids                                             quadrilaterals
the properties of trapezoids                     *determine properties of trapezoids with respect to parallel sides, length     trapezoid
• Quadrilateral                                  of sides, diagonal measurements, and measurement of angles                     consecutive sides/angles
• One pair of opposite sides are parallel        *explore trapezoids and their properties to verify the type of figure formed   opposite sides/angles
• Midsegment is half the sum of the lengths of                                                                                  midsegments
the bases

Resources:                 G. 8-6 pg.439; patty paper wkst 76 and 84

Assessments:

Page 18 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
R.4.G.1h                   Explore, verify and solve problems involving    *identify properties of isosceles trapezoids                               quadrilaterals
the properties of isosceles trapezoids          *determine properties of isosceles trapezoids with respect to parallel     trapezoid
• Same properties as trapezoids                 sides, length of sides, diagonal measurements, and measurement of          isosceles trapezoid
• Non-parallel opposite sides (legs) are        angles                                                                     consecutive sides/angles
congruent                                       *explore isosceles trapezoids and their properties to verify the type of   opposite sides/angles
• Base angles are congruent                     figure formed                                                              midsegments
• Diagonals are congruent                                                                                                  diagonals

Resources:                 G. 8-6 pg.439; supplemental with patty paper

Assessments:
R.4.G.1i                   Explore, verify and solve problems involving    *identify properties of kites                                              quadrilaterals
the properties of kites                         *determine properties of kites with respect to parallel sides, length of   kite
• Quadrilateral                                 sides, diagonal measurements, and measurement of angles                    consecutive sides/angles
• Two pairs of adjacent sides are congruent     *explore kites and their properties to verify the type of figure formed    opposite sides/angles
• No opposite sides are congruent                                                                                          diagonals
• Diagonals are perpendicular                                                                                              perpendicular

Assessments:
5b. Essential Question - How are the properties of polygons used to find angle measures and number of sides?
R.4.G.2a                   Solve problems involving the sum of the         *classify polygons based on the number of sides                            polygons
measures of the interior angles of a polygon    *identify regular and irregular polygons                                   consecutive sides
and the interior angle measure of regular and   *identify concave and convex polygons                                      interior angles of a polygon
irregular polygons                              *determine the sum of the interior angles of several polygons to derive    regular polygon, including
the formula                                                                pentagon, hexagon, heptagon,
*use the formula for determining the sum of the interior angles            octagon, decagon
*calculate an interior angle of a regular polygons                         irregular polygon
*calculate a missing interior angle of a polygon given the other angles    concave polygon
*given the total degrees of the interior angles, determine the number of   convex polygon
sides or angles of a polygon
*solve problems using properties of polygons

Resources:                 G. 8-1 pg.404; Manipulatives pg.128; Ch.8 Resources pg.422; wkst. Concave and Convex Polygons; wkst Finding the Sum of the Interior Angles of a
Polygon; wkst The Big Quadrilateral Puzzle; patty paper wkst 56

Page 19 of 40                                                               Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
Assessments:
R.4.G.2b                   Solve problems involving the exterior angles   *recognize that the sum of exterior angles of any polygon is 360 degrees     polygons
of a regular or irregular polygon              *calculate an exterior angle of a regular polygons                           consecutive sides
*calculate a missing exterior angle of a polygon given the other angles      interior angles of a polygon
*given the total degrees of each exterior angle, determine the number of     exterior angle of a polygon
sides or angles of a polygon                                                 regular polygon, including
*solve problems using properties of polygons                                 pentagon, hexagon, heptagon,
octagon, decagon
irregular polygon
concave polygon
convex polygon

Resources:                 G. 8-1 pg.404; Ch.8 Resources pg.418; wkst Polygons and Formulas

Assessments:
R.4.G.2c                   Solve problems involving the number of sides *calculate a missing interior or exterior angle of a polygon given the other   polygons
and number of angles of a polygon            angles                                                                         consecutive sides
*given the total degrees of the interior angles, or the degrees of each        interior angles of a polygon
exterior angle, determine the number of sides or angles of a polygon           exterior angle of a polygon
*solve problems using properties of polygons                                   regular polygon, including
pentagon, hexagon, heptagon,
octagon, decagon
irregular polygon
concave polygon
convex polygon

Resources:                 G. 8-1 pg.404; problems pg.407 21-26

Assessments:
5c. Essential Question - What determines a polygon and how are they used?

Page 20 of 40                                                              Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
CGT.5.G.5                 Based on properties of polygons, determine      *classify polygons based on their properties                                  parallelogram
the type of figure formed from a given set of   *use the distance formula to determine lengths of sides and diagonals of      isosceles triangle
points                                          a polygon                                                                     trapezoid
*use the slope formula to determine parallel and perpendicular sides and      rectangle
diagonals of polygons                                                         square
*determine the types of figures based on their properties, when given a       rhombus
set of points plotted in the coordinate plane                                 scalene triangle
equilateral triangle
kite
regular polygons
distance formula
slope formula
slopes of parallel and or
perpendicular lines
National Core:            G.SRT.1                                         Verify experimentally the properties of dilations given by a center and
a scale factor: (a.) A dilation takes a line not passing through the center
of the dilation to a parallel line, and leaves a line passing through the
center unchanged. (b.) The dilation of a line segment is longer or shorter
in the ratio given by the scale factor.

Resources:                G. 8-7 pg.447; pg.429 problems 27-29; pg.437 problems 53-56; pg.442 problems 9-12; Ch.8 Resource pg.442; wkst. Coordinating Polygons

Assessments:
20 SLEs                                                                                                                                                                     End of Module 1

ALIGNMENT NOTES
Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together
Project for Module 4

Page 21 of 40                                                               Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
GEOMETRY                  PULASKI CO. SPEC. SCHOOL DIST.                                                                                                          2010 - 2011
Module 5     Start: 2/7/2011 Teaching Days: 22              Test: 3/17/2011      Remediation Days: 1 End: 3/11/2011
Student Learning Expectation                                                    Task Analysis                                              Vocabulary

6. Enduring Understanding - Geometric transformations form mappings.
6a. Essential Question - How are geometric transformations mapped from the preimage to the image?
CGT.5.G.7a              Draw and interpret the results of              *define translation, reflection, and rotation                             transformation
transformations on figures in the coordinate   *identify transformations                                                 line of symmetry
plane using translations, reflections, and     *draw translations, reflections, and rotations                            translations
rotations (90°, 180°, clockwise and            *draw, apply and interpret transformations transformations in the         reflections
counterclockwise about the origin)             coordinate plane                                                          rotations
clockwise
counter-clockwise

National Core:          G.CO.2                                         Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that
take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch).

G.CO.5                                         Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or
geometry software. Specify a sequence of transformations that will
carry a given figure onto another.

Resources:              G. 9-1 pg.463; 9-2 pg.470; 9-3 pg.473; 9-4 pg.483; supplemental material booklets on transformations

Assessments:

Page 22 of 40                                                              Glencoe Geometry: 2005                                              127rgeorge@pcssdmail.org
CGT.5.G.7b              Draw and interpret the results of dilations   *define dilation                                                              dilations
(scale factor) and successive dilations on    *draw and interpret the results of dilations and successive dilations         successive dilations
figures in the coordinate plane                                                                                             scale factor

National Core:          G.SRT.1                                       Verify experimentally the properties of dilations given by a center and
a scale factor: (a.) A dilation takes a line not passing through the center
of the dilation to a parallel line, and leaves a line passing through the
center unchanged. (b.) The dilation of a line segment is longer or shorter
in the ratio given by the scale factor.

G.CO.2                                        Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that
take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch).

G.CO.5                                        Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or
geometry software. Specify a sequence of transformations that will
carry a given figure onto another.

Resources:              G. 9-5 pg.490; supplemental cartoons; wkst. Working with a Scale

Assessments:

Page 23 of 40                                                             Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
CGT.5.G.7c              Draw and interpret the results of successive       *define translation, reflection, rotation, and dilation                       transformation
transformations on figures in the coordinate       *identify transformations                                                     line of symmetry
plane (Ex. translations, reflections, rotations,   *draw translations, reflections, rotations, and dilations                     successive transformations
and dilations)                                     *draw, apply and interpret transformations and successive                     translations
transformations in the coordinate plane                                       reflections
rotations
dilations
clockwise
counter-clockwise

National Core:          G.SRT.1                                            Verify experimentally the properties of dilations given by a center and
a scale factor: (a.) A dilation takes a line not passing through the center
of the dilation to a parallel line, and leaves a line passing through the
center unchanged. (b.) The dilation of a line segment is longer or shorter
in the ratio given by the scale factor.

G.CO.2                                             Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that
take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch).

G.CO.5                                             Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or
geometry software. Specify a sequence of transformations that will
carry a given figure onto another.

Page 24 of 40                                                                  Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
Resources:                MCO---Students will work in groups to use graph paper or white marker boards to graph transformations. Students will discuss the strategy used and the
change in the x and y coordinate.

Assessments:
7. Enduring Understanding - Attributes of geometric figures affect their ability to tessellate.
7a. Essential Question - What determines if a geometric figure will tessellate?
R.4.G.3                   Identify and explain why figures tessellate       *determine the measure of an interior angle of a polygon                tessellation
*define tessellate
*determine through exploration that angle measures of polygons which
will tessellate must be factors of 360 degrees
*identify figures which will tessellate and why

Resources:                G. 9-4 pg.483; have students do their own tessellation; patty paper wkst 180-187;     MCO---Student will research the drawings of Dutch artist M.C. Escher
and create their own tesselation.

Assessments:
4. Enduring Understanding - Indirect measure is based on properties of geometric figures
4c. Essential Question - How are areas of ploygons and circles related and applied?
M.3.G.1                   Calculate probabilities arising in geometric      *write ratios                                                           probability
contexts (Ex. find the probability of hitting a   *find perimeter and areas of polygons                                   area
particular ring on a dartboard)                   *find circumference and areas of circles                                ratio
*compare area, perimeter, and circumference of basic shapes
*use ratios to find percentages
*solve proportions to find probability of hitting a target

Resources:                G. 11-5 pg.622 ; MCO----Student will use shaded parts of a game board (darts, checkers, etc) or scale drawing of a tennis or basketball court to calculate
the probabilities.

Assessments:
8. Enduring Understanding - Three dimensional figures have properties similar to those of 2 dimensional figures.

8a. Essential Question - How are two-dimensional relationships connected to properties of three-dimensional figures?

Page 25 of 40                                                                Glencoe Geometry: 2005                                              127rgeorge@pcssdmail.org
R.4.G.4                    Identify the attributes of the five Platonic     *recognize and name the five platonic solids                              platonic solids
Solids                                           *identify the polygons that form the faces of the platonic solids         tetrahedron
*define faces, vertices, and edges and determine the number of each for   dodecahedron
the platonic solids                                                       icosahedron
*identify the attributes of the five platonic solids                      hexahedron
octahedron
cube
regular polyhedron

Resources:                 G. 12-1 pg.636; supplemental nets and figures; wkst Types of Solids

Assessments:
R.4.G.7a                   Use orthographic drawings (top, front, side) to *given views of a three-dimensional object, draw and/or identify the       foundation drawing
represent three-dimensional objects             complete object                                                            orthographic drawing
*draw the 2-dimensional and foundation views of three-dimensional
objects

Resources:
Assessments:
R.4.G.7b                   Use isometric drawings (corner) to represent     *given views of a three-dimensional object, draw and/or identify the      isometric drawing
three-dimensional objects                        complete object
*draw the views of three-dimensional objects
*draw and interpret isometric drawings

Resources:                 G. 12-1 pg.640; Ch.12 Resources pg.666;        MCO----Students will work in groups to make orthographic and isometic drawing using stacked blocks and
isometric dot paper.

Assessments:

Page 26 of 40                                                               Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
R.4.G.8                   Draw, examine, and classify cross-sections of Prerequisite Skills:                                                        cross-section
three-dimensional objects                     •identify three-dimensional figures
•identify polygons and circles

*identify ellipses
*draw cross-sections of three- dimensional objects
*examine and classify by naming the resulting two-dimensional cross-
section
*draw and classify the results of cross-sections of three-dimensional
objects

National Core:            G.GMD.4                                         Identify the shapes of two-dimensional cross-sections of three-
dimensional objects, and identify three-dimensional objects generated
by rotations of two-dimensional objects.

Resources:                G. 12-1 pg.640; problems pg.640 25-30; MCO---- Students will work in groups to make cross-sections using Play-DOh or Styrofoam.

Assessments:
9. Enduring Understanding - Practical problems can be interpreted, represented, and solved using formulas.

9a. Essential Question - How are geometric formulas applied to solve basic and application problems.

M.3.G.2b                  Solve application problems involving area of    *use estimations and exact values in area of circles                      area
circles, polygons and composite figures using   *convert between units of measure                                         polygon
appropriate units and formulas and expressing   *substitute and evaluate expressions                                      circle
solutions in both approximate and exact forms   *recognize two-dimensional figures                                        composite figure
(include apothem of a regular polygon)          *use square unit representation, and understand when it is used           apothem
*apply appropriate formulas to find area of two- dimensional shapes and   concentric circles
composite shapes (Resource: EOC Mathematics Reference Sheet)
*solve application problems

National Core:            G.MG.2                                          Apply concepts of density based on area and volume in modeling
situations (e.g., persons per square mile, BTUs per cubic foot).

Resources:                Area:G. 11-1 pg.595; 11-2 pg.601; 11-3 pg.610; pg.11-4 pg.617; geoboards; wkst. Finding Area- Painting a Room; wkst. Finding Area-Tiling a Floor; wkst
Finding Area-Fertilizing a Lawn; wkst. Comparing Areas; patty paper wkst 205

Page 27 of 40                                                              Glencoe Geometry: 2005                                                127rgeorge@pcssdmail.org
Assessments:
M.3.G.2c                   Solve application problems involving surface     *use estimations and exact values in finding surface area               area
area of prisms, cylinders, pyramids, and cones   *convert between units of measure                                       surface area
using appropriate units and formulas and         *substitute and evaluate expressions                                    polygon
expressing solutions in both approximate and     *recognize two- and three-dimensional figures                           prism
exact forms                                      *use square unit representation, and understand when it is used         pyramid
*apply appropriate formulas to find surface area of three-dimensional   cone
shapes and composite shapes (Resource: EOC Mathematics Reference        cylinder
Sheet)                                                                  composite figure
*solve application problems                                             apothem
concentric circles
National Core:             G.MG.2                                           Apply concepts of density based on area and volume in modeling
situations (e.g., persons per square mile, BTUs per cubic foot).

Resources:                 Surface Area: G. 12-2 pg.643; 12-3 pg.649; 12-4 pg.655; 12-5 pg.660; 12-6 pg.666; 12-1 pg. 636 use nets to make 3-dimensional figures; wkst. Surface
Area and Wrapping Paper;; MCO---- Students will work in groups to measure and find the surface area and volume of various empty food containers.

Assessments:
M.3.G.2d                   Solve application problems involving surface     *use estimation and exact values when finding surface area              area
area of composite figures using appropriate      *convert between units or measure                                       surface area
units and formulas and expressing solutions in   *substitute and evaluate expressions                                    polygon
both approximate and exact forms                 *recognize two- and three-dimensional figures                           prism
*use square unit representation, and understand when itis used          pyramid
*apply appropriate formulas to find surface area of three-dimensional   cone
shapes and composite shapes (Resource: EOC Mathematics Reference        cylinder
Sheet)                                                                  sphere
*solve application problems                                             composite figure
apothem
concentric circles
National Core:             G.MG.2                                           Apply concepts of density based on area and volume in modeling
situations (e.g., persons per square mile, BTUs per cubic foot).
Resources:                 Surface Area: G. 12-2 pg.643; 12-3 pg.649; 12-4 pg.655; 12-5 pg.660; 12-6 pg.666; 12-1 pg. 636 use nets to make 3-dimensional figures; wkst. Surface
Area and Wrapping Paper;; MCO---- Students will work in groups to measure and find the surface area and volume of various empty food containers.

Assessments:
12 SLEs                                                                                                                                                                  End of Module 1

ALIGNMENT NOTES
Notation

Page 28 of 40                                                               Glencoe Geometry: 2005                                              127rgeorge@pcssdmail.org
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together
Project for Module 5

Page 29 of 40                           Glencoe Geometry: 2005   127rgeorge@pcssdmail.org
GEOMETRY                     PULASKI CO. SPEC. SCHOOL DIST.                                                                                                              2010 - 2011
Module 6       Start: 2/14/2011 Teaching Days: 28               Test: 5/5/2011       Remediation Days: 1 End: 5/5/2011
Student Learning Expectation                                                      Task Analysis                                              Vocabulary
9. Enduring Understanding - Practical problems can be interpreted, represented, and solved using formulas.

9a cont.. Essential Question - How are geometric formulas applied to solve basic and application problems.

M.3.G.2e                   Solve application problems involving volume     *use estimations and exact values when finding volume                    volume
of prisms, cylinders, pyramids, and cones       *convert between units of measure                                        polygon
using appropriate units and formulas and        *substitute and evaluate expressions                                     prism
expressing solutions in both approximate and    *recognize three-dimensional figures                                     pyramid
exact forms                                     *use cubic unit representation, and understand when it is used           cone
*apply appropriate formulas to find volume of three-dimensional shapes   cylinder
and composite shapes (Resource: EOC Mathematics Reference Sheet)         composite figure
*solve application problems                                              apothem
concentric circles
National Core:             G.GMD.3                                      Use volume formulas for cylinders, pyramids, cones, and spheres to
solve problems.
Resources:                 Volume: G. 13-1 pg.688; 13-2 pg.696; differentiated instruction pg.698; teacher to teacher pg.699; wkst. Volumes of Containers;

Assessments:
M.3.G.2f                   Solve application problems involving volume     *use estimations and exact values when finding volume                    volume
of composite figures using appropriate units    *convert between units of measure                                        polygon
and formulas and expressing solutions in both   *substitute and evaluate expressions                                     prism
approximate and exact forms                     *recognize three-dimensional figures                                     pyramid
*use cubic unit representation, and understand when it is used           cone
*apply appropriate formulas to find volume of three-dimensional shapes   cylinder
and composite shapes (Resource: EOC Mathematics Reference Sheet)         sphere
*solve application problems                                              composite figure
apothem
concentric circles
National Core:             G.GMD.3                                         Use volume formulas for cylinders, pyramids, cones, and spheres to
solve problems.
Resources:                 G.pg.699 problems 17-19

Assessments:

Page 30 of 40                                                              Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
M.3.G.2g                   Solve application problems involving surface     *use estimations and exact values in surface area and volume of spheres         area
area and volume of spheres using appropriate     *convert between units of measure                                               volume
units and formulas and expressing solutions in   *substitute and evaluate expressions                                            surface area
both approximate and exact forms                 *recognize three-dimensional figures                                            polygon
*use square and cubic unit representation, and understand when each is          sphere
used                                                                            composite figure
*apply appropriate formulas to find volume and surface area of three-           apothem
dimensional shapes and composite shapes (Resource: EOC Mathematics              concentric circles
Reference Sheet)
*solve application problems

National Core:             G.GMD.3                                          Use volume formulas for cylinders, pyramids, cones, and spheres to
solve problems.
G.GMD.2                                          (+) Give an informal argument using Cavalieri’s principle for the
formulas for the volume of a sphere and other solid figures.

Resources:                 G. 12-7 pg.671; 13-3 pg.703; wkst. Creating Problems and Applying Formulas (Advanced); MCO---Investigate careers in the U.S. and other cultures that
solve problems of area, perimeter and volume.

Assessments:
10. Enduring Understanding - Relationships exist among angles, arcs, and segments of circles.

10a. Essential Question - How are circle formulas applied to solve basic and application problems.

R.4.G.5a                   Solve problems involving the measure of          *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
central angles, the relationship between         *apply relationships of congruent chords and their arcs, and use those          inscribed angle
congruent central angles , the relationship      relationships to solve problems                                                 arc
between congruent chords and the measure         *apply relationship of central angles and their arcs to solve problems          chord
of the arcs they intercept and vice versa        *calculate angles and arc measures of interior angles of a circle               circle
point of tangency
diameter

National Core:             G.C.1                                            Prove that all circles are similar.
G.C.2                                            Identify and describe relationships among inscribed angles, radii,
and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles;
the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.

G.C.3                                            Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.

Page 31 of 40                                                                 Glencoe Geometry: 2005                                                    127rgeorge@pcssdmail.org
Resources:                 G. 10-2 pg.529; wkst Drawing Circles; wkst Circles:Symbols of Segments and Angles; wkst The Big Circle Puzzle

Assessments:
R.4.G.5b                   Solve problems involving the relationship         *identify chords, central angles, radii, interior angles, and arcs            central angle
between a radius that is perpendicular to a       *apply relationship of central angles and their arcs to solve problems        inscribed angle
chord in a circle and the size of the resulting   *calculate angles and arc measures of interior angles of a circle involving   arc
segments of the chord                             the relationship between a radius that is perpendicular to a chord            chord
circle
diameter
perpendicular
National Core:             G.C.1                                             Prove that all circles are similar.
G.C.2                                             Identify and describe relationships among inscribed angles, radii,
and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles;
the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.

G.C.3                                             Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.

Resources:                 G. 10-3 pg.536; Manipulatives pg.164; MCO---Students will be given regular triangles, squares, pentagons, etc. to cut out. At a vertex point on another
sheet of paper, students will gllue a shape around the point to see if there is a gap or overlap. Students will find the measure of an interior angle and divide
into 360. Repeat the process for all polygons.
Assessments:
R.4.G.5c                   Solve problems involving the congruence          *identify chords and arcs                                                      central angle
relationship of two chords in a circle which are *understand relationships of congruent chords and their arcs, and use          inscribed angle
equidistant from the center and vice versa       those relationships to solve problems                                          arc
*calculate chords and arc measures of a circle                                 chord
circle
diameter

National Core:             G.C.1                                             Prove that all circles are similar.
G.C.2                                             Identify and describe relationships among inscribed angles, radii,
and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles;
the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.

G.C.3                                             Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.

Page 32 of 40                                                                  Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
Resources:                 G. 10-3 pg.536

Assessments:
R.4.G.5d                   Solve problems involving the relationship       *identify chords, central angles, interior angles, inscribed angles, and arcs central angle
between measure of an angle inscribed in a      *apply relationship of central angles and their arcs to solve problems        inscribed angle
circle and the measure of the intercepted arc   involving inscribed angles                                                    arc
*calculate angles and arc measures of inscribed angles of a circle            chord
circle
diameter

National Core:             G.C.1                                           Prove that all circles are similar.
G.C.2                                           Identify and describe relationships among inscribed angles, radii,
and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles;
the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.

G.C.3                                           Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.
Resources:                 G. 10-4 pg.544; Manipulatives pg.167-169

Assessments:
R.4.G.5e                   Solve problems involving the perpendicular     *identify central angles, interior angles, and arcs                           central angle
relationship between a tangent to a circle and *understand relationship of central angles and their arcs                     arc
a radius drawn to the point of tangency        *identify tangents of a circle                                                tangent
*define point of tangency                                                     tangent to a circle
*apply the relationship between a tangent and a radius or diameter at         circle
point of tangency, and use that relationship to solve problems                point of tangency
diameter
perpendicular
National Core:             G.C.4                                           (+) Construct a tangent line from a point outside a given circle to the
circle.
Resources:                 G. 10-5 pg.552; Manipulatives pg.174-175; Ch.10 Resources pg.569; wkst Tangents: Circles and Lines; wkst. The Bigger Circle Puzzle

Assessments:

Page 33 of 40                                                               Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
R.4.G.5f                   Solve problems involving the congruence of   *identify interior angles, inscribed angles, and arcs                            central angle
two segments from the same exterior point of *apply relationship of central angles and their arcs to solve problems           inscribed angle
a circle that are tangent to a circle        involving tangents to a circle from a common point                               arc
*recognize tangents of a circle                                                  tangent
*define point of tangency                                                        tangent to a circle
*apply relationships of tangents and use those relationships to solve            circle
problems                                                                         point of tangency
diameter

National Core:             G.C.4                                         (+) Construct a tangent line from a point outside a given circle to the
circle.
Resources:                 G. 10-5 pg.552; Ch.10 Resources pg.568

Assessments:
R.4.G.5g                   Solve problems involving the measure of an    *identify chords, central angles, interior angles, and arcs                     central angle
angle formed by the intersection of two       *apply relationships of congruent chords and their arcs, and use those          inscribed angle
chords within a circle                        relationships to solve problems                                                 arc
*apply relationship of central angles and their arcs                            chord
*calculate angles and arc measures of interior angles of a circle               circle
diameter

Resources:                 G. 10-6 pg.561; problems pg,564 12-15,20
Assessments:
R.4.G.5h                   Solve problems involving the measure of an    *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
angle formed by a secant and a tangent        *apply relationships of congruent chords and their arcs, and use those          inscribed angle
intersecting at the point of tangency         relationships to solve problems                                                 arc
*apply relationship of central angles and their arcs to calculate angles and    chord
arc measures of interior angles of a circle                                     tangent
*identify tangents and secants of a circle                                      tangent to a circle
*define point of tangency                                                       secant
*understand relationships of tangent and secant segments, and use those         circle
relationships to solve problems                                                 point of tangency
diameter
Resources:                 G. 10-6 pg.561; Ch.10 Resources pg.576
Assessments:

Page 34 of 40                                                             Glencoe Geometry: 2005                                                     127rgeorge@pcssdmail.org
R.4.G.5i                   Solve problems involving the measure of an      *identify chords, secents, tangents, and arcs                                   arc
angle formed by two intersecting secants, a     *identify tangents and secants of a circle                                      tangent
secant and a tangent, or two tangents           *define point of tangency                                                       tangent to a circle
intersecting in the exterior of a circle        *apply relationships of tangent and secant segments, and use those              secant
relationships to solve problems                                                 point of tangency
diameter

National Core:             G.C.4                                          (+) Construct a tangent line from a point outside a given circle to the
circle.
Resources:                 G. 10-6 pg.561; wkst. The Biggest Circle Puzzle
Assessments:
R.4.G.5j                   Solve problems involving the measure of the     *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
segments formed by two intersecting chords      *understand relationships of congruent chords and their arcs, and use           inscribed angle
in a circle                                     those relationships to solve problems                                           arc
*understand relationship of central angles and their arcs                       chord
*calculate segment lengths of intersecting chords of a circle                   circle
diameter

Resources:                 G. 10-7 pg.569; Ch.10 Resources pg. 582
Assessments:
R.4.G.5k                   Solve problems involving the measure of the     *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
tangent segment, the secant segment, and        *understand relationships of congruent chords and their arcs, and use           inscribed angle
the external segment of the secant when a       those relationships to solve problems                                           arc
tangent and secant are drawn to a circle from   *apply relationship of central angles and their arcs to solve problems          chord
the same exterior point and the measure of      *identify tangents and secants of a circle                                      tangent
the secant segments and the external            *define point of tangency                                                       tangent to a circle
segments formed by two secants to a circle      *understand the relationship between a tangent and a radius or diameter         secant
intersecting at an external point from the      at point of tangency, and use that relationship to solve problems               circle
circle                                          *understand relationships of tangent and secant segments, and use those         point of tangency
diameter

Resources:                 G. 10-6 pg.561; G. 10-7 pg.569

Assessments:

Page 35 of 40                                                               Glencoe Geometry: 2005                                                     127rgeorge@pcssdmail.org
R.4.G.5l                   Solve problems involving the area of sectors    *find the area and circumference of a circle                                  circumference
and the lengths of arcs                         *identify sector area and arc lengh                                           central angle
*use relationships of parts of circles to determine areas of sectors          arc
*use the relationships of parts of circles to determine the length of a given chord
arc                                                                           circle
diameter
sector
Resources:                 G. pg.532; G. pg.623-624

Assessments:
R.4.G.6                    Solve problems using inscribed and              *identify inscribed and circumscribed figures                               inscribed figure (circle or polygon)
circumscribed figures                           *find areas of polygons and circles to solve problems                       circumscribed figure (circle or
*find incenter and circumcenter of triangles                                polygon)
*solve problems using inscribed and circumscribed figures                   incenter
circumcenter

National Core:             G.CO.13                                         Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
Resources:                 G. 11-3 pg. 610; Manipulatives pg.185; wkst Inscribed Polygons
Assessments:
M.3.G.2a                   Solve application problems involving            Prerequisite Skills:                                                        circumference
circumference, and perimeter of polygons and    •use estimations and exact values in circumference of circles               perimeter
composite figures using appropriate units and   •convert between units of measure                                           polygon
formulas and expressing solutions in both       •substitute and evaluate expressions                                        circle
approximate and exact forms                     •recognize two-dimensional figures                                          composite figure
•use linear unit representation, and understand when it is used             apothem
concentric circles
*apply appropriate formulas to find perimeter/circumference of two-
dimensional shapes and composite shapes (Resource: EOC Mathematics
Reference Sheet)
*solve application problems
Resources:                 G. Ch.1 Resource pg 36; 10-1 pg.522; Manipulatives pg.161 find pi using circles(donuts,cookies,soda cans, use dental floss for measurement tool with
rulers); wkst. Finding perimeter -Fencing a Yard;

Assessments:
11a. Essential Question - How can the relationship between points on a circle be described in the coordinate plane?

Page 36 of 40                                                               Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
CGT.5.G.6a                Write the equation of a circle in standard form *recognize the standard form of the equation of a circle                   standard form of an equation for
given a graph on a coordinate plane and vice *identify the center of a circle and determine the length of its radius given a circle
versa                                           a graph                                                                    circle
*write the standard form of the equation of the circle                     center of a circle
*use the Pythagorean Theorem to derive the standard form of the            radius
equation of a circle                                                       diameter
National Core:            G.GPE.1                                         Derive the equation of a circle of given center and radius using the
Pythagorean Theorem; complete the square to find the center and
radius of a circle given by an equation.
Resources:                G. 10-8 pg.575
Assessments:
CGT.5.G.6b                Write the equation of a circle in standard form *recognize the standard form of the equation of a circle                   standard form of an equation for
given the center and radius and vice versa      *write the standard form of the equation of a circle given the center and a circle
*write the standard form of the equation of the circle                     center of a circle
*use the distance formula to derive the standard form of the equation of a radius
circle                                                                     diameter
National Core:            G.GPE.1                                        Derive the equation of a circle of given center and radius using the
Pythagorean Theorem; complete the square to find the center and
radius of a circle given by an equation.
Assessments:
18 SLEs                                                                                                                                                                  End of Module 1

ALIGNMENT NOTES
Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together
Project for Module 6

Page 37 of 40                                                              Glencoe Geometry: 2005                                                127rgeorge@pcssdmail.org
Click on the links to open the following
PDF files

8_by_8_numbered_grids

10_by_10_numbered_grids

grids_not_numbered

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isometric_grids

6_square_dot_grids

logic_grids

plain_graph_paper

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EOC Mathematics Reference Sheet
GEOMETRY   PULASKI CO. SPEC. SCHOOL DIST.   2010-2011

National Core Standards
NOT CURRENTLY PLACED IN THE CURRICULUM

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